His side were on the back foot for the opening 10 minutes of the match, until Samuel Eto'o's shot took a very helpful deflection over David De Gea to make it 1-0. Eto'o doubled the lead just before half time, and he completed his first hat-trick in English football shortly after the break.
Javier Hernandez gave United hope with 10 minutes left to play, but the comeback never materialised. Nemanja Vidic's red card in injury time compounded the visitors' misery, and they were lucky to end the game with 10 men as Rafael committed a horrendous foul on Gary Cahill.
Chelsea cruised to this comprehensive victory, and Twitter users were quick to add their comments to the post-match discussion.
A recruitment agency used David Moyes' predicament at United for this topical advert:
Some users made jokes at Moyes' expense:
David Moyes to star in new reality tv show "I'm A Calamity, Get Me Eto'o here" #MoyesIn— Footy banter thingy (@rimsey_d) January 19, 2014
While one fan of Football Manager empathised with him:
And others made Eto'o the star of the show:
If Luis Suarez scores a hattrick against you, fair enough. If a 32 year old Samuel Eto'o does, you're in serious trouble— Bergkamp is gÖd (@Orangeiceman10) January 19, 2014
There was also an excellent reminder to be careful what you say on Twitter:
"@DannyDoes: If Samuel Eto'o scores a hat-trick, I will get a tattoo of his face." HAHAHAHAHAAHAHHAAHAHAHAHAHAHAHAHAHAHAHAH— Chelsea Talk (@ChelseaTalkMarc) January 19, 2014
The post-match interview with John Terry and Samuel Eto'o went down a storm:
LOOOOOL Cheslea 3-1 Man Utd - Samuel Eto'o Speaks French While John Terry Translate for him....: http://t.co/pVJIWEf5gt— TeamChelseaFC (@TeamChelseaFC) January 19, 2014
Mourinho's hundredth victory threw up some great stats:
100 - Both Jose Mourinho's first and 100th Premier League wins have come against Manchester United at Stamford Bridge. Nemesis.— OptaJoe (@OptaJoe) January 19, 2014
Jose Mourinho is the quickest to get to 100 #BPL wins. Top 5: Mourinho 142 matches, Ferguson 162, Wenger 179, Benitez 181, Dalglish 197— Premier League (@premierleague) January 19, 2014
And Opta Joe had another couple of gems up his sleeve:
5 - Manchester United have gained only five points in nine games against other top eight sides this season. Stutter. pic.twitter.com/TVDAIp4Nat— OptaJoe (@OptaJoe) January 19, 2014
With the "Moyes Out" hashtag trending again, one Twitter user dug this out of the archives:
A rational approach indeed.
Despite all that, the tweet that summed up the afternoon best came from Mark Worrall:
Short match report - Chelsea won, United didn't— Mark Worrall (@gate17marco) January 19, 2014
If you feel that there was an excellent tweet missing from this list, you can let me know in the comments below, or on Twitter itself.